Hi,
could you please tell me how to find the answer
1)How many numbers greater than 200 can be formed using the numbers (0,2,4,6,8)
could you please tell me how to find the answer
1)How many numbers greater than 200 can be formed using the numbers (0,2,4,6,8)
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I assume each number can only be used once.
If that is not the case, the answer will easily be infinite, since 222, 2222, 22222, 222222 are all numbers greater than 200.
Since the number 200 is a 3 digit number, all numbers greater than it must have at least 3 digits.
Case 1 (3 digit numbers):
Clearly 0 cannot be the first digit, so we are left with 2, 4, 6 and 8 to be the first digits.
Thus, we have 4 options.
For the second digit, we can choose 0 as an option now.
Thus, we still have 4 options if we include the 3 remaining option from the first part.
For the third digit, we have 3 digits left, so we simply have 3 options.
Thus, the amount of 3 digits number greater than 200 is
= 4 * 4 * 3
= 48
Note that since 0 cannot be used twice, no matter what number we form starting with 2, it will still be greater than 200.
Case 2 (4 digit numbers)
Once again, for the 1st digit, we have 4 options (since we cannot choose 0).
The 2nd digit will also consist of 4 options (since we put back 0 as an option).
The 3rd digit will have 3 options, and the 4th digit will have 2 options.
Thus, the amount of 4 digits number greater than 200 is
= 4 * 4 * 3 * 2
= 96
Case 3 (5 digit number)
This case is similar to the 4 digit number case.
We have 4 options for the 1st digit (since we cannot choose 0).
The 2nd digit will also consist of 4 options (since we put back 0 as an option).
The 3rd digit will have 3 options, the 4th digit will have 2 options, and we will only have 1 option for the 5th digit.
Thus, the amount of 5 digits number greater than 200 is
= 4 * 4 * 3 * 2 * 1
= 96
Hence, the total amount of numbers greater than 200 which can be formed is
= 48 + 96 + 96
= 240 numbers
If that is not the case, the answer will easily be infinite, since 222, 2222, 22222, 222222 are all numbers greater than 200.
Since the number 200 is a 3 digit number, all numbers greater than it must have at least 3 digits.
Case 1 (3 digit numbers):
Clearly 0 cannot be the first digit, so we are left with 2, 4, 6 and 8 to be the first digits.
Thus, we have 4 options.
For the second digit, we can choose 0 as an option now.
Thus, we still have 4 options if we include the 3 remaining option from the first part.
For the third digit, we have 3 digits left, so we simply have 3 options.
Thus, the amount of 3 digits number greater than 200 is
= 4 * 4 * 3
= 48
Note that since 0 cannot be used twice, no matter what number we form starting with 2, it will still be greater than 200.
Case 2 (4 digit numbers)
Once again, for the 1st digit, we have 4 options (since we cannot choose 0).
The 2nd digit will also consist of 4 options (since we put back 0 as an option).
The 3rd digit will have 3 options, and the 4th digit will have 2 options.
Thus, the amount of 4 digits number greater than 200 is
= 4 * 4 * 3 * 2
= 96
Case 3 (5 digit number)
This case is similar to the 4 digit number case.
We have 4 options for the 1st digit (since we cannot choose 0).
The 2nd digit will also consist of 4 options (since we put back 0 as an option).
The 3rd digit will have 3 options, the 4th digit will have 2 options, and we will only have 1 option for the 5th digit.
Thus, the amount of 5 digits number greater than 200 is
= 4 * 4 * 3 * 2 * 1
= 96
Hence, the total amount of numbers greater than 200 which can be formed is
= 48 + 96 + 96
= 240 numbers